Lectures related to Essential Adjoints: Spectral Decomposition and Symmetric Operators

Explains the postulates of quantum mechanics and the representation of observables by operators.

Explores the theory of bounded operators on Hilbert space, including adjoint properties and self-adjointness.

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Explores the spectral decomposition of self-adjoint operators on Hilbert spaces.

Covers the essential concepts of adjoint operators, spectrum, and resolvent sets in operator theory.

Explains the postulates of Quantum Mechanics, focusing on self-adjoint operators and mathematical notation.

Covers the axioms of quantum mechanics and the measurement of quantities in a quantum system.

Covers fundamental concepts in quantum mechanics, including vector spaces, superposition, observables, and inner product.

Explores the postulates of Quantum Mechanics, emphasizing the state of a system as a complex-valued vector in a Hilbert space.

Explores the spectral decomposition of non-bounded operators and presents the spectral theorem for self-adjoint non-bounded operators.

Explores vector spaces, linear transformations, matrices, eigenvalues, inner products, and operators.

Covers the duality principle in linear algebra and its implications in mathematics.

Offers a crash course on quantum mechanics, covering vector spaces, superposition, observables, and self-adjoint operators.

Explores the definition and properties of the functional calculus for self-adjoint and bounded operators.

Introduces the postulates of Quantum Mechanics, focusing on states in a Hilbert space and the role of observables.

Explores the matrix representation of operators and basis transformation in linear algebra.

Covers self-adjoint operators, Weyl criterion, and functional calculus in the context of symmetric operators and real spectrum.

Explores eigenvalue problems, eigenbasis, spectral theorem, and properties of normal operators.

Covers the fundamental concepts of unbounded operators and their adjoints, exploring auto-adjoint and normal operators.

Explores Hermitian operators, auto-adjoint properties, and spectral theorems in Hermitian spaces.